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Byzantine-robust Federated Learning (FL) aims to counter malicious clients and train an accurate global model while maintaining an extremely low attack success rate. Most existing systems, however, are only robust when most of the clients are honest. FLTrust (NDSS '21) and Zeno++ (ICML '20) do not make such an honest majority assumption but can only be applied to scenarios where the server is provided with an auxiliary dataset used to filter malicious updates. FLAME (USENIX '22) and EIFFeL (CCS '22) maintain the semi-honest majority assumption to guarantee robustness and the confidentiality of updates. It is therefore currently impossible to ensure Byzantine robustness and confidentiality of updates without assuming a semi-honest majority. To tackle this problem, we propose a novel Byzantine-robust and privacy-preserving FL system, called MUDGUARD, that can operate under malicious minority \emph{or majority} in both the server and client sides. Based on DBSCAN, we design a new method for extracting features from model updates via pairwise adjusted cosine similarity to boost the accuracy of the resulting clustering. To thwart attacks from a malicious majority, we develop a method called \textit{Model Segmentation}, that aggregates together only the updates from within a cluster, sending the corresponding model only to the clients of the corresponding cluster. The fundamental idea is that even if malicious clients are in their majority, their poisoned updates cannot harm benign clients if they are confined only within the malicious cluster. We also leverage multiple cryptographic tools to conduct clustering without sacrificing training correctness and updates confidentiality. We present a detailed security proof and empirical evaluation along with a convergence analysis for MUDGUARD.